Determine the no of natural numbers smaller than 104,in the decimal notation of which all the digits are distinct - Maths - Permutations and Combinations

Question

Determine the no of natural numbers smaller than 104,in
the decimal notation of which all the digits are distinct?pls solve
this question by fundamental principle of counting rather than
permutations?

Anuradha Sharma · Accepted Answer

Hi, The fundamental principal of counting is not possible here due to lengthy process
SO permutaion method is best
The required natural number consists of 4, digits, 3-digits, 2-digits, 1-digits
Total number of 4-digit natural number with distinct digit = 10P4-9P3Total number of 3-digit natural number with distinct digit = 10P3-9P2Total number of 2-digit natural number with distinct digit = 10P2-9P1Total number of 1-digit natural number with distinct digit = 10P1-9P0So the required number of natural number =10P4-9P3+10P3-9P2+10P2-9P1+9=5274

Determine the no. of natural numbers smaller than 104,in the decimal notation of which all the digits are distinct?pls solve this question by fundamental principle of counting rather than permutations?

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